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Ya'll correct me if I'm wrong

The COP is a term that has to do with the fact that a heat pump will produce less capacity at lower temps. I believe the COP is just a reference to electric heat with a COP of 1.
But, I don't think it can be related as you are trying to do. The COP is more of an output term rather than an input term. You will still be paying the same amount on your utility bill, but you won't be getting as much out.

North, this is probably more of a question myself, than an answer.
At 47 degrees, yur heat pump will be using ( pretty much ) the same electricity, but you will not be getting the same BTU's out, and the unit will run longer, costing you more money

The COP, is an output rating.
Copared to the 100% eff. of electric resistance heat.
A 3.5 cop at 47 means that compared to resistance heat, he will be getting 3.5 times more heat per kw consumed, then resistance heat.

Or 10KWH of resistance heat =34130btu
And 2.857KWH of heat pump =34128.94btu at 3.5 cop provided that is his heat pumps btu, and cop rating.

Yep, you are on track. There are some other variables to consider, primarily defrost cycle.

On my own house I have the electric resistance heat cutoff with a big relay that only closes if the outside temp is below 25F (almost never in Seattle area).

So, during a defrost cycle, there is cold air coming out of the registers, but DW and I live with that. What really puts a "hurt" on your simple COP calculation is that 5 minutes every 1/2 hour that 10kW of resistance heat kicks in. If you live witht the short cold air blast, that expense is also reduced by the COP ratio. If you are in a dry area, you may never go into defrost anyway, but the HP sure does here in PNW.

Moral of story, you are $$ ahead to turn the breaker for the resistance heat section of your air handler off, turn it on only when its so cold outside you cannot heat otherwise. On current HP on own house (with the outside thermo control as above) in Seattle area, have never had resistance heat kick in except for a test.

COP is short for coefficient of performance. So this means that the HP is working at 350% efficient compared to electric strips when it is 47deg. So for $.08 you get 34,130 btus with strips. When the heat pump is working in 47 degree air it will give you 34,130 x 3.5 = 119,455 btus for the $.08. The higher the air temp. the higher the COP, the lower the air temp the lower the COP. Most air sourse HP have a 1 COP at about -10 degrees.

Thanks everyone else as well. I realize that the COP drops as the outside temp. drops. This heat pump (Amana) has a COP of 2.4 at 17 degrees. I also realize that there are some variables in there that will affect the actual COP such as defrost cycle etc.

But the crux of the matter is that compared to a 95 % efficient gas furnace that the heat pump will be in the neigborhood of 200 to 300 % efficient even if natural gas is a little cheaper initially than electricity the heat pump will be cheaper to operate year in year out by a fairly wide marging I would guess.